Trains are cheap and decent between the bigger cities but the real gems like the Transfagarasan highway and those tiny mountain villages are basically impossible to reach on public transport without wasting a whole day. Dropping some extra cash to rent a car in Romania means you can pull over at random castles and roadside food stops instead of watching them blur past a train window. You can dig into the available options and see what fits your route here
https://getrentacar.com/en-US/romania .